In a regression model my dependent variable is a count variable that can have negative numbers. 
So let's say the dependent variable it's the subset of integer numbers from -5 to 5.

What econometric method can I use? Poisson regression and negative binomial only accept positive dependent variable

In particular, the dependent variable it's the difference in the number of managers of a company after and before an investment round. So a value of 2 indicates that there are 2 more managers, while a value of -2 indicates that there 2 less managers